I doubt it. Most newer games still fallback to some OpenGL 1.x for compatibility reasons. Even StarWars:KoTOR2 The Sith Lords uses OpenGL 1.4 - I finished it a week ago.
As for Doom3 I played it both under my GF4 Ti4200 and current ATi Radeon 9600 and played fine on both.
Now, it's probably right to think that some of the newest games may use some newer OpenGL 2.0 extensions (and more than games, demos). I don't know what would happen when you run them on a older card. They will probably switch to some compatibility mode still, or they may leave those new "bell and whistles" behind (advanced options grayed out?).
PS - As a sidenote, OpenGL is GREAT. I will never get accostumed to the behemoth slow Direct-X powered game engines (VALVe Source(tm) engine comes to mind). They are simply quite slow when compared to OpenGL, although there are always some exceptions that break the rule (although rare). Some other people say OpenGL is faster but Direct-X is more evolved and has better "eye-candy". I am not entirely sure.
Intel i7 5960X
Gigabye GA-X99-Gaming 5
8 GB DDR4 (2100)
8 GB GeForce GTX 1070 G1 Gaming (Gigabyte)